Opportunistic cognitive radio broadcast channel: Asymptotic performance

We consider a cognitive channel where one secondary transmitter opportunistically broadcasts to n secondary nodes subject to peak interference power constraints on the primary receivers. We find asymptotic bounds for the secondary throughput, which imply that the throughput scales as Θ(log log n) for any finite interference constraint, no matter how small. Furthermore, a fundamental tradeoff between the secondary throughput and the interference on the primary is obtained, showing that the interference on the primary can be forced asymptotically to zero while maintaining a nontrivial secondary throughput. Specifically, for an arbitrary exponent 0 < q < 1, the interference on the primary can be made as small as (logn)−q, while the secondary throughput scales as (1-q) log log n+O(1). Finally, if the number of primary receivers increases as Θ(nβ), the secondary system attains only a constant throughput asymptotically, for any β > 0.